Complementary filter



Oct. 13, 1925. 1,557,230

o. J. zoBEL COMPLEMENTARY FILTER Filed April 30 l 1920 5 SheeiS-Shee' l ATTORNEY Oct. 13, 1925. 1,557,230

5? 52 7 mi l? if INVENTOIL d 0. J ZUM CL mmm' Oct. 13, 1925-- 1,557,230

. o. J. zoBEL COMPLEMENTARY FLTER A T TO R N E Y Patented Oct. 13, 1925.

UNITED STATES Pr-ALTENT (.)FFICE OTTO J. ZOIBEL, OF MAPLEV/'OODy NEVI JERSEY, "SSEGNR TO AMERICAN TELEPHONE AND TELES-BAPE COMPAITY, PI OGREBATIGN F NEW YORK.

Application filed April 8U. 1926.

To all fr0/wm t may concern:

Be it ltnoufn that I. @Tru J. Konan, residing at h'Iaplewood. in the iounty ot Esse); and State of New Uerseyz have invent-ed ecrtain Iniproveinents in Complementary Filters, of which the 'followingv is epe-,cineation.

rIlhis invention relates to selective circuits, and inore particularl5.Y to selective circuits of the type linowu as wave filters.

In certain types of transmission circuits, where it has been desired to separate the diiilerent frequency cur ents transmitted over a line into two channels. it has heen found convenient to produce the separation hy ,means ot wave Vfilters oit 'the general type disclosed iu the Il, patrnts to George A. amphell, Nos. 1,2 4,119, ann l QllLl1 issued May 1917. For example. a socalled high pass tllter might he used in one channel. and a so-called low pass filter iniejht,

he used in the other channel.. the high pass lilter transmitting' all currents ahove a certain frequency and the low pass tilter trausiuitting; all currents helow a desired trequency. In such cases. tho 'traml ion and attenuation :frequency regions 'loA the wave filter used in one channel should he approximately the reverse ot those tor the wave filter in the other channel. In other words, the v ave filters should he comple- Inentary.

In general. when a wave 'filter is connected in a circuit whose impedance is a practically constant resistance laroje impedance irregularities are introduced hetvr n the wave `lilter and the circuit in the rango ot trequencies to he transmitted.. since the characteristic impedance of the tilter at any termination varies lgreatly with freouency. These impedance irregularities at the trequencies to he transmitted. are ohiectionaole not only 'from the standpoint ot maximum energy transferred from the circuit to the wave filter, but also from the standpoint ot repeater balance. I have found. hows ever. that certain types of wave filters. it properly designed, will have characteristics such that over the rane'e of tree tran is- MPLEMENTARY FILTER.

Serial No. 3??,965.

staat. The wave filter having this characteristie is known constant 712 filter. ifrnioue' other filters, the so-called high pass and low pass .filters ot the Campbell type naar he so designed as to he constant 7u Filters.

In general, when two wave lill ers are connected in series or parallel, at the transmitting' iii ,quency of either wave lter, the total impedance ot the two wave Vfilters is not a constant resistance, which would be ideal. hut varies greatly with frequency. It is possibler` however`r to ohtain a practically constant resistance tor the conihined iinpedances ot two such complementary wave lters at all trequencies except those in the neiehhorlmod of the critical 'frequencies ot the wave liltors, provided the filters are coinpleinontary constant 1 types7 where the series and shunt elements ot the one type are proportional respectively to the shunt and series elements ot the other type. @ne ot the principal ohj'iects oit the invention is to produce circuit arrangement which will secure the result just stated. altluuieh other and 'further ohjects ot the invention will more vtully r )pear hereinafter.

the li approximately constant over the rar ot tree transmission and equal to a cons I have also Ytound that with complementary constant 1 types, where two wave tilters are used together in the manner previously stated. they inay he so terminated that either one approximate- .lv tul'lls the rle oi the proper impedance corrective network for the other. Thus, Ytrom an impedance standpoint. there is a heueticial interference ot one wave iilter upon the other. rl'lhis assumes that there are no larrfje irreeularities on the drop side ot either wavel filter at frequencies which it transmits. except those 'frequencies near the critical treuuencies. The condition is easily t'ulhlled with constant 7c types ot filters by using' impedance corrective networks upon thtx drop sides of the filters.

.It will. he shown that when two complementary constant 7c wave filters are put in series, this result may he secured hy termii nating the filters in aJ-shunt, and when the filters are in parallel, the same result may be secured by tern'iinating the filters in .fcseries, where and a is an arbitrary constantI usually taken as 4 or slightly greater. Bv an shunt termination of a lfilter is meant such a termination of the filter that the shunt element of the last section ot the filter is an admittance, which is a fractional part ot the full series admittance of a normal shunt element7 said Ytraction being represented by In other words, it the impedance ot the normal shunt element be represented by the terminal shunt impedance will be By an crc-series termination is meant such a termination of the filter that the impedance of the series element of' the last section will be a fractional part ot the impedance ot a full series element, a; representing the traction as before. Thus7 if the impedance of a normal series element b@ repre Vnted by el, the impedance ot the terminal series elcment will be wel.

The wave filters forming' the subject matter ot this invention have a periodic structure consisting; ot a plurality ot sections as shown in Fig. 2, each section coniprisiuej series and shunt in'ipedance elenientf-:- These impedance elements are reactanccs, that is, they are made up ot inductances and capacities in a manner more fully described hereafter. lVhile the discussion et these wave filters is primarily on a basis that the elements are non-dissipative in charznfter.` the inevitable introduction of dissipation will not materially alter the designs obtained. ln order to minimize the transmission losses in the wave filter' there should be provided as largo time constants Ytor the iuductances and capacities as is practicable in each specific case.

The computation for the filter on the assinned basis that its rcactances are nou-dissipative is justified both by theoretical investigations and by practical tests. lt is well known that the resistance ot a coil or condenser can be made very small coinpared to its inductive reactance or capacity reactance, and therefore the performance of such a coil or condenser may be computed approximately with entire neglect ot such slight resistance. l

The invention may now be more fully understood by reference to the followingr detailed description, when read in connection with the accompanying drawings., in Which Figure 1 is a series of curves exhibiting certain characteristics of constant lo wave filters; Fig. 2 is a schematic diagram ot a wave filter terminating in .a1-series; Fig, 3 is a schematic diagram showin;T a form of terminal networlit'or matting the impedance ot the filter equal to a constant resistance; Fig. 4 is a schematic diagram of a wave filter terminatingr in Lnshunt; Fig. 5 is a schematic diagram ot a. corresponding terminal network tor securing' the same results as in the case of Fig. fl; Fig'. G is a simplified diagram sliowiimv how two complementary filters may be connected in series; Fig'. 7 is a si allai' diagram showing' how the filters may be connected in parallel; Fig'. 8 is a diagram similar to Fie". 7 but showingl the film s terminated on the drop side by networks to ren-der their inipedances from that side equivalent to a substantially constant resistance: Fie'. 9 a diagran'i similar to Fig. S and shon'infr how complementary filters may be used for interconnerting two cir. s to a certain range Ot frequencies; while i equencies outside the range transmitted over either circuit will be diverted into other channels; and Fie'. l() is a diagram o't complementary high pass and low pass filters connected in parallel in accordance with the invention.

ln order to secure the results sought by this present invention. two things are necessary: first. the deteriaiuation of" the desired complementary constant 1 type of filter corresponding to a known constant 1 type. and second. the impedance corrective design which .cjives the in'oger method ot terlninatine' these filters when combined in series or parallel so that th total in'ipedauce remains practically a conf resistance over most oit the rane-e of 'fi .e rtransn'iission.

.in order that these designs may be obtained, it is nef'issarv to consider certain theory under yinlsr the principles ot wave transmis i ln connection with this thecry?, a description will he given of two methots of t rminatingr any constant le wave filter, so that the resiiltine` corrected impedance is substantially a constant resistance i7: throughout the transmitting range ot the wave fil i For the best correction one method terminates the wave filter in .S09- series, (that in a series elen'ient whose impedance is 900 times that of a full series element), and adds in shunt, a shunt annulling element consiisting ot in series with 3.23622. The other method terminates the network in .SOQ-shunt. (that is, in a shunt element whose admittance is .809 times that of a full shunt element), and adds in series, a series annulling element consisting of .30921 in shunt with 9c- The theory underlying these impedance corrective designs is as follows:

It is well known that a smooth line having uniform series impedance distributions e, and uniform shunt impedance distribin tions per unit. length, has the characteristie iinpedai'ice i: wits i and a propagation constant A Wave lilter such as illustrated in Fig. 6, havingseries elenients e, and shunt clen'ients 2g has a characteristic impedance at any terinination which is a function oit both the product and ratio ot .2', and and has propagation constant which is a tiinction ot' their ratio. Hence it has been Yfound convenient to express both the characteristic impedance and propagation constant ot the Wave ilter in terins of 7n and y, the parameters ot the correspondingl sniootli line. As pointed out in the Campbell patent above referred to, free transmission occurs in s cli wave filters, (if innitely long) tor a range ot i'irequein cies corresponding to the range Let us now determine the :v-series characteristic admittance, A, et a Wave filter, having a series eleinent .el and a shunt elenient z2 per section. Referring to the dia- 72=0 to y2: i.

Axe

Since, as explained iu the Campbell patent7 at transmitted Yfrequencies y lies between O and i?? and is inifigfginary, it follows that, :troni the formula oit equation 8, the first hallc of the right hand portion of equation 8 represents the conductance (the conductance being' positive), and the last halt represents the susceptance (the susceptance being contained in the imaginary terni). Hence We have H2172 i Cxsztm (10) and isxs: mll l (ii) NOW it is apparent that the susceptance inay be annulled in equation 8 by a shunt annul- J5 This expression, by simple algebraic transiorniation may be expressed l" A lr l H /j'xs 75 )Z1 It *ni Z152 JV T21 (D) -10 New since the admittance is the reciproci" el the impedance, we have ,i l l l LXSS fijn-l?? 'vf f y 1 Xs l 1w 12g-tte? -I- (QJ- .0)21

lultiglying' both numerator and denoininator by 5 O 21g- *l* 'Z1" (fC Z1 .r

We get n l 2 r f rr i@ 2122-11-,21 +Le-.w21 o@ AY =-wgm--m-mfnff" 7 ts zlsz-l-Ml-@zf e Replacing` by y and c1-22 by k2 we have (g) i -i-xU. -9:)fy2 7c lingg eleinent ot equal value and opposite in sign to the Value of the susceptauce given in equation li. The admittance fia, ot he shunt eleineiit iniist then be 1+'(1' l" 10o Since the impedance Za. ot the annulling elenient is the reciprocal ot the admittance l or f equation l2 inay be rewritten by subsli l r stituting` thc value ot y and 7i' as :tollows: 100

Z2 @(1 t rl' f) n in is sh ,v a, r 1

lli-oni the torni ot this equation it is apparent that the shunt annulling` eleinent conl l0 sists oi' two parts in series-one part having an impedance *'15 115 and the other part having an impedance rc(1 wel.

This only holds true when ai is greater than .5, because it :c is less than .5, these quantities becoine negative and cannot be realized physically. The circuit arrangement of a filter terminating in -series, and having a shunt annulling element contermin(y to e nation 13 is illustrated schematically in g. 23 In the arrangement of Fig. 3, it .r is greater than .5, and

the shunt aniiull Y element is provided, there left only the first part of the admittance oit the filter, which, in the transmitting range, is the coiuluetance Cw. The conh ductance eoeflicient may be Written as fiollouis:

nearly equal to and the impedance to t:

constant in the transmitting range.

Ve Will new determine the proper impedance corrective design for a filter having an x-shunt termination. Such a filter is indicated schematically in Fig. 4, and from this figure it is apparent that the a-shunt impedance ZW, may be Written as follows:

The impedance Z of a filter havingl a full series termination may, from Fig. 4, be eX- pressed as follows:

zzZ 22 Z Substituting this value of Z in formula 15, We have, by simple algebraic transformations Zz iU\/Z13z t Multiplying both numerator and denominator by mz 2 22 'll fl? `/Z1Zz'i z`21) and simplying, We have Zxsh (1 7) Substituting the values of q' and 7c, this equation becomes l #,Lnl/y- Substituting the values of y and in equation 20, We have, by simple algebraic transtorination Frein equation 2l it is apparent that the annulling element may consist of two parallel elements. Whose impedances are (fU-.5)z1 and respectively when a: is greater than .5.

This arrangement is illustrated in Fig. 5, and When provided it is obvious that only the first part et the impedance ot the filter reii'iains, this part in the transmitting range being the resistance Rxsh. The resistance eoeffieient is the saine coefficient as given in equation 14, and from F ig. 1 is nearly unity over the greater part ot the transmitting range, When fc has a value about .8. Hence with a teri'i'iination ot .8 shunt, the resistance Rm, will, in the constant 7c types of filters, be substantially equal to 713 in the transmitting range.

From equations 13 and 21 it .is apparent that a constant 7c type of filter may be terminated by either a series or shunt :innulling element, having such characteristics that the impedance of the filter over the transmitting range will be practically equal to a constant resist-ance. In practice, it is found that a desirable value fior the factor in these equations is .809, which not only has the advantage of being near .8, which as shown in Fig. 1 is the mest desirable value, but also permits of a similarity in the elements of both shunt and series annulling networks. This value ot .fr is chosen because then .t l-i .521

.521, it will be noted, is the value of the tei'- minal series element in a mid-series termination of a wave filter which is. practice, a very common forni of termina jor wave filters. The value oi .1' aliove given 'therefore, permits oi using,Y a half series element oic the filter as one of' theI elements of the annullinfgj network.

Leaving for the moment the design of terminating networks for filters, whereby they may be given constant impedance values, let us determine the desifijn ot' desired complementary constant 7c wave filters independently of how they may ce terminated. Let el and z2 be respectively the series and shunt impedance eleii'ients per section ot' a known constant la wave filter, havingl the required transmission and attenuation re- `ggions, where 21- z2 k2 2 constant (23) The complementary constant le type of filter may now be obtained from .al and .e2 by putting' its series element el proportional to .e2 and its shunt element e2 proportional to el. 1We will then have Z1] (LZ2 and (24) gi z'A l a lies between O and *4, and its complementary type transmits when 21 22 lies between the same limits. tion 24 it is apparent that From equa- Hence to the frequency range at which the known wave filter transmits, that is, to the range limiting y2 between 0 and 41, there corresponds in the complementary constant 7c wave filter a range This range niay or may not include part of the transmitting range of the known wave `filter, depending upon the particular value chosen for en Thus, if c is less than t, the transmitting ranges of the two wave filters will overlap, vfor then y2 will be greater than --l-z if a equals el, the ranges just touch each other; and ii a is greater than al, the ranges are separated leaving' a region in between where neither filter transmits, for in this case. y will be less than met. In practice, it is usually desirable to have the transmitting regions just touching or slightly separated. Hence, the value ol a will usually be t or a slightly larger value.

Having` now determined the design of two roniplementary wave filters, we will next elucidate the manner in which the compleiiwiitai;r wave filters may be terminated in order that their' total impedance, when connected in series oi' in parallel, will become practically a constant resistance, except near the critical trequencies. The methods of terminating the filters follow from a consideration of' the method of impedance cori'ection by means of corrective or annulling networks previously developed. lThe terminations for either a parallel o1` series connection are so chosen that one wave filter acts to a certain extent as a terminal annullinp` network for the other at the free transmitting frequencies of the latter.

Taking up first the case of two compleinentary wave filters connected in series as indicated in Fig. 6, it will be apparent from equation 2l et seq., that if the constant le filter, each of whose sections comprises series elements e', and shunt elements e2, be terminated in .ca-shunt by means of a 2 shunt element the imaginary part of its impedance may be neutralized by including` in series with its terminal section a combination of two impedances in parallel. Now, in Fig. 6 it will be seen that the filter el', 5., may be considered to form such a combination, if

which forms the .fc-shunt termination of the filter be considered one of the parallel impedances and the remainder of the filter be considered the other impedance iii parallel therewith. `We will then have, from equation 124i-, an impedance a; am

as one parallel impedance of an annullinp,- network, while the other impedance will be an impedance somewhat greater than elraez. This shunt combination will be somewhat similar to the shunt combination called for by equation 2l et seq. at the transinitting frequencies of the lilter' al, e2, provided we put Solving this equation, We get lt a; be given the value called tor by equation 28, then the m-shunt terminal element oit the lower liltei' of Fig. (S ivill correspond exactly to one ot the tivo parallel impedanees required to malte the impeoaiice ot the upper i'ilter a constant resistance over its transmitting` range. lt a i be made equal 'to l, which ls previously explained would be the value assigned to it vvlicre 'the trans4 mission ranges of the tirei'ilters just touch each other, u iii equation 28 will have the value .809, which as already explained, is the value Which gives an approximately constant resistance equal to L except near the critical frequencies. A larger value ot' the arbitrary constant i i will, ot course, give a smaller value of w. For this value of as it ivill be not-ed that the inipeda` ce of that portion ot the lower filter in Fig. (l, which is in parallel with the element will be somewhat greater than is called tor by equation 2l et seq. However, over the transmitting` range oli the upper ilter7 the element plays a much larger part in determining the impedance ot the parallel annullin@` coinbination than docs trie much laigger .impedance oil" the remainder ot the louer filter. Conseqiientiy7 ivhilc the desired result is only approximate so fai as the second parallel element ct the aniiullingij combination is roncerned, the api ri'ixiniation su'iiciently close that the lower tilter will., to all intents and purposes, serre as an annulling element tor the upper lilter.

By converse line ot reasoning, it is clear that a similar approxinnition is reached wlien the com .ilementary ivavc filter el, e2 is considered transmitting, the upper iilter in this case serving as the annullingnetwork. Equation QS may he deduced for this converse relation and the tivo wave tilters may therefore he made to mutually al each other as renards iinoedance correction when lt will be seen trom Fig. 7 that the .fa-series element ot the loier .filter may tunction one or" the series impedances ot the annulling combinationA` this element having' from equation Qt the Value fcelzfeazg. The 'remainder of the loiver tiltei constitutes a second impedance in series with thel first impedance oi" the annulling combination7 the second impedance having a value some` what less than rlhis series combination ot inipedances Will correspond somewhat to the series combination called tor by equation lil at thc transmitting frequencies of the upper filter, provided. ive put ;t21=afez2=* (30) o By solving equation B09 we will again ob tain equation Q8, so that should have the same value as in the parallel arrangement of Fig. G. As before, it a be made equal to a, C0 ivill have the value .809. For this value.. the element wel will exactly correspon-fl to the requirements ot the first ele inent ot equation 13. The remainder of the lower filter will not have the saine impedance as called lor by the second halt ot equation lil. Sincev` hou'ei'er, over the transmitting' range et the upper filter oit Fi 7, the eleent wel plays tl e largest in deteimining` the iinpeiflance ot the iulliin';v combination, it is not so essen* tial that the iinnedance olf the remainder ot the ilter conform exactly to the requirements ot equation 13.

As previously stated, for the best operation ot tivo filters in parallel7 or in series, the ends et the liltcrs opposite to their junction points, or in other Words, the drop sides ot the filters should also be so terminated as to cause the impedance of each filter viewed 'from the drop side to he substantially a constant resistance over the range ol transmission of the lilter. Accordingly, in Fig. 8, two filters are shown connected together in parallel so 'that each acts as an annulling element for the other, the two filters being connected to av circuit conventionally indicated as a resistance It at the left hand side of the figure. rl`hc dotted lines indicate that a large number Of sections may intervene between the junction points of the filters and their drop sides. The filters upon their drop sides are ter minated in '.r-seiies as indicated, und annulling elements constructed in accordance with equation i3 are provided to eliminate the reactance components of' the impedance. The drop impedance Zd of' the upper filter and the drop impedance Zd of the lower filter may each be made, therefore, substantially equal at transmitted frequencies to the re- 'spective` resistances R and lt of the circuits to which the lters are connected.

The complete impedance corrective arrangement for the interconnection of parallel complementary constant 7c wave lilA ters is illustrated in Fig. 9. In accordance with the arrangement of this figure, a line made up of two sections, each having a re sistance R may be connected to terminals l, 2 and 5, 6 respectively, so that the upper wave filter of the figure interconnects the two sections of the line for transmission at certain frequencies. In a similar manner, another linel made up of two sections each having a resistance R may be connected to terminals 3, 4 and 7, S so that the two sections of the line may be interconnected for transmission at certain frequencies by means of the lower filter of the series. A third filter is connected between terminals l, 2 and 3, 4t so that one section oit one line may transmit at other frequencies to another section of the other line. y this means. two lines which are independently transmitting currents of certain frequencies, may be connected at some given intermediate point, so as to transmit from one end of one line to one end of' the other line currents of other frequencies, without causing interference between these different independent currents. The drop sides of the upper and lower filters are terminated by shunt annulling elements designed in accordance with equation 13, while the ends of the upper pair of filters connected to the terminals l, 2 are so terminated and related to each other that the filters, being complementary, act as annulling elements for each other. The same is true of the lower pair of filters at the terminals 23, 4.

In all of the filter arrangements so far described, the shunt and series elements are conventionally indicated as iinpedances and it will be understood that in practice, these iinpedances may be made up of inductances and capacities in various relations. Thus, in Fig. 6, if the upper filter is a low pass filter, the elements e, willbe inductauces and the elements capacities. ln this case, the lower lter will be the high pass filter so that the elements e, will be capacities and the elements inducances. Such an arrangement ot' high pass and low pass filters is indicatetl` in Fig. lf), in which ih" normal series element of each tion of the upper filter is an inductance ,1. and the shunt element is a capacity C2. i' n. noruuil series element of each section of the lower filter is a capacity C1 while the shunt clement is an inductance fi. The filters are lterminated in afl-series where a', has a value of .Sta/l, The drop sides of the filter are terminate-'l by shunt annulling elements couqu' C the case of the upper 'filter an inductance and a capacity G2G. and in the case of lower filter, au inductancc ,d and a` capacity Gld. The values of these elements will be once obtainable 'from a l. In this particular filter de; the u( shunt element adjacent to thc ju iti ion point of' the two filters, instead of hav: t the nor mal shunt value, is altered somewhat as indicated by the values C2 in the case ot the upper filter, and

in the case of the lower filter. fu both iustances, rc2 has a value of about .96. ft has been found 'that by making this change in the last shunt element of cach complementary filter, the filters will more nearly approach the requirements of the ideal annulling elements as given in equation ffl, Vl'lach filter, therefore, will more closely approxi mate the ideal condition so far as its bencficial impedance effect upon the other filter is concerned.

It will be obvious that the general principles herein disclosed may be embodied in many other organizations widely different from those illustrated without departing from the spirit of the invention as defined in the following claims.

i/Vhat is claimed isl. A selective circuit comprising a plurality of filters, each consisting of a plurality of like sections, and each section including shunt and series impedance elements, the filters being joined at one end of each so that certain frequencies may be diverted into gne filter, and other frequencies into anotherV filter, the lters at the junction point being terminated respectively in fractional sections so proportioned that for the free transmitting range of each filter the remaining filter or filters operate to reduce im pedance irregularities of said each filter.

2. A selectivo circuit comprising a plurality of filters, each consisting of a plurality of like sections, and each section including shunt and series impedance elements, the fil- CSI lll

sections so Dio terminal d so propelVH ilters at the junction respectarelyv in tractior f tioned that over ortion o the iree transn'iitting l the feniaining hiter or render 'the in'ipedance of J ibstantially t ual to a c q nce.

Yz selective cir/cv singin pluralilu filters, each 'ng of e plurality oii like sections and each section including shunt and series impedance elen'ients, lt being' joined at one end quencies may be diverted d oth r "reunen-oies into i, the liiters at the junction yerminated respectively in traeropoi so thaA into one another nl point being; 1

cional sections so p oned that over s l Yaially the entire range of free transi of.l earn tilter, the remaining filter or filters operate a an annulling elementto annul the reactance component oit the inipedance.

A selective circuit comprising tivo i eonsistingv et a plurality of like id each section including shunt i impedffnce elements, said ilters y joined one endL so that certain frequencies may be diverted into the one filter and other freqinencie;-'J into the other filter,

l secti ons a said lilters at the junction point being each terminated in a iractional section so proreactence if over siibstantialljY the entire range ansinission.

` a tri nsnjiission linl and i filters connected therea fd filter having;i a fractional end iooriiined to correi make the peinte as a reactance annulthe other filter.

ation7 a 'transmission line and ot' complementary filters c011- `\vith, cach said filter having a sectioi proportioned to make a cictit any one of them i y z a ieactance :umullingl network 'or that one litter.

1"n combination, a transmission line, jiu

ers connected therewith, the transil in-'i of one corresponding to the of the other and vice i Vter having; an m-fractional 'i i toward the line, i ith o? equal to i 'hereby each filter with such fraciination acts as a reactance annulin combination, a transmission line, a

pl ot filters connected therewith, each lil er ha ving a respective transmission band to; a treruency range lying within the suppression ranges for all the other filters, and all said i'ilters except any one of them being j'iroportione/,l and designed to serve as a reactance annullingl network for such one lilter.

l0. ,ln combination, a transmission line and a plurality ot tilters with respective eX- clusive transinisun'in ranges, said assembly of filters having' a resultant impedance substantially equal to the line impedance for frequencies within any one of the transmission anges in testimony whereof, I, have signed my naine to this specification this 28th day of April 1920.

OTT() J. ZOBEL. 

